问3道初中提公因式的题.

题目

问3道初中提公因式的题.
1.若（x-1)(x+3)(x-4)(x-8)+m是完全平方式,求m
2.若a+2b+3c=12,且 a平方+b平方+c平方=ab+bc+ca,则a+b平方+c立方=?
3.已知x不等一,且x立方-x=5,y立方-y5.求x平方+xy+y平方的值

答案

1.(x-1)(x-4)(x+3)(x-8)+m=(x²-5x+4)(x²-5x-24)+m
令x²-5x=A,原式为（A+4)(A-24)+m=A²-20A-96+m
根据配方法,A²-20A+100=(A-10)²,所以-96+m=100,m=196
2.两边同时×2得：2a²+2b²+2c²=2ab+2ac+2bc,2a²-2ab+2b²-2bc+2c²-2ac=0
a²-2ab+b²+(b²-2bc+c²)+(c²-2ac+a²)=0 即 (a-b)²+(b-c)²+(a-c)²=0
∴a=b=c,又有a+2b+3c=12,故都为2.a+b²+c＾3=2+4+8=14
3.x＾3-x=5,y＾3-y=5.
x＾3-x-(y＾3-y)
=(x＾3-y＾3)x+y
=(x＾3-y＾3)-(x-y)
=(x-y)(x²+xy+y²)-(x-y)
=(x-y)(x²+xy+y²-1)=5-5=0
∵x≠y ∴x²+xy+y²-1=0.x²+xy+y²=1